The seventh-seeded Craybas, who reached the quarter-finals in Rome last week, had to work before emerging with a 6-2 3-6 6-4 triumph over Tzipora Obziler of Israel.
Ranked just 116th in the world, King also needed three sets on the red clay to move into the next round. She posted a 6-1 6-7 (1-7) 6-3 victory over Alla Kudryavstseva of Russia.
King won her lone career meeting against Craybas with a three-set victory on the hard courts in Bangkok in 2007.
Fourth-seeded Olga Govortsova of Belarus cruised into the second round with a 6-3 6-2 rout of Ipek Senoglu of Turkey.
It was a short stay for fifth-seeded Swede Sophia Arvidsson, who dropped a 6-3 7-6 (7-2) decision to Andreja Klepac of Slovenia.
Unseeded players to advance Monday were Aiko Nakamura, Stephanie Dubois, Nathalie Vierin and Marta Domachowska.
The top seed here is defending champion Elena Dementieva. The Russian is the only top-10 player in this French Open tune-up event.